USIN TOOL S Use technology to evaluate $$ (f+g)(x),(f-g)(x),(f g)(x) $$, and $$ \left(\frac{f}{g}\right)(x) $$ when $$ x=5 $$. Round your answers to two decimal places. $$ f(x)=-2 x^{1 / 3} ; g(x)=5 x^{1 / 2} $$ $$ (f+g)(5)=\square $$ $$ (f-g)(5)=\square $$ $$ (f g)(5)=\square $$ $$ \left(\frac{f}{g}\right)(5)=\square $$

Question

UpStudy AI · Accepted Answer

Evaluate the expression by following steps:
- step0: Evaluate:
  $$-2x^{\frac{1}{3}}-5x^{\frac{1}{2}}$$
- step1: Substitute:
  $$-2\times 5^{\frac{1}{3}}-5\times 5^{\frac{1}{2}}$$
- step2: Calculate:
  $$-2\times 5^{\frac{1}{3}}-5^{\frac{3}{2}}$$
- step3: Simplify:
  $$-2\sqrt[3]{5}-5^{\frac{3}{2}}$$
- step4: Simplify:
  $$-2\sqrt[3]{5}-5\sqrt{5}$$
Substitute $$ x=5 $$ into the expression $$ -2*(x)^{1/3}+5*(x)^{1/2} $$.
Evaluate the expression by following steps:
- step0: Evaluate:
  $$-2x^{\frac{1}{3}}+5x^{\frac{1}{2}}$$
- step1: Substitute:
  $$-2\times 5^{\frac{1}{3}}+5\times 5^{\frac{1}{2}}$$
- step2: Calculate:
  $$-2\times 5^{\frac{1}{3}}+5^{\frac{3}{2}}$$
- step3: Simplify:
  $$-2\sqrt[3]{5}+5^{\frac{3}{2}}$$
- step4: Simplify:
  $$-2\sqrt[3]{5}+5\sqrt{5}$$
Substitute $$ x=5 $$ into the expression $$ -2*(x)^{1/3}/(5*(x)^{1/2}) $$.
Evaluate the expression by following steps:
- step0: Evaluate:
  $$\frac{-2x^{\frac{1}{3}}}{\left(5x^{\frac{1}{2}}\right)}$$
- step1: Substitute:
  $$\frac{-2\times 5^{\frac{1}{3}}}{\left(5\times 5^{\frac{1}{2}}\right)}$$
- step2: Calculate:
  $$\frac{-2\times 5^{\frac{1}{3}}}{5^{\frac{3}{2}}}$$
- step3: Rewrite the fraction:
  $$-\frac{2\times 5^{\frac{1}{3}}}{5^{\frac{3}{2}}}$$
- step4: Simplify:
  $$-\frac{2\sqrt[3]{5}}{5^{\frac{3}{2}}}$$
- step5: Simplify:
  $$-\frac{2\sqrt[3]{5}}{5\sqrt{5}}$$
- step6: Multiply by the Conjugate:
  $$\frac{-2\sqrt[3]{5}\times \sqrt{5}}{5\sqrt{5}\times \sqrt{5}}$$
- step7: Multiply the numbers:
  $$\frac{-2\sqrt[6]{3125}}{5\sqrt{5}\times \sqrt{5}}$$
- step8: Multiply the numbers:
  $$\frac{-2\sqrt[6]{3125}}{25}$$
- step9: Calculate:
  $$-\frac{2\sqrt[6]{3125}}{25}$$
Substitute $$ x=5 $$ into the expression $$ -2*(x)^{1/3}*5*(x)^{1/2} $$.
Evaluate the expression by following steps:
- step0: Evaluate:
  $$-2x^{\frac{1}{3}}\times 5x^{\frac{1}{2}}$$
- step1: Substitute:
  $$-2\times 5^{\frac{1}{3}}\times 5\times 5^{\frac{1}{2}}$$
- step2: Multiply the terms:
  $$-2\times 5^{\frac{1}{3}+1+\frac{1}{2}}$$
- step3: Add the numbers:
  $$-2\times 5^{\frac{11}{6}}$$
- step4: Rewrite the expression:
  $$-2\times 5\sqrt[6]{5^{5}}$$
- step5: Calculate:
  $$-2\times 5\sqrt[6]{3125}$$
- step6: Calculate:
  $$-10\sqrt[6]{3125}$$
Let's evaluate the expressions step by step using the given functions $$ f(x) = -2x^{1/3} $$ and $$ g(x) = 5x^{1/2} $$ at $$ x = 5 $$.

1. **Calculate $$ (f + g)(5) $$**:
   $$
   (f + g)(5) = f(5) + g(5) = -2(5)^{1/3} + 5(5)^{1/2}
   $$
   Evaluating this gives:
   $$
   (f + g)(5) \approx 7.76
   $$

2. **Calculate $$ (f - g)(5) $$**:
   $$
   (f - g)(5) = f(5) - g(5) = -2(5)^{1/3} - 5(5)^{1/2}
   $$
   Evaluating this gives:
   $$
   (f - g)(5) \approx -14.60
   $$

3. **Calculate $$ (fg)(5) $$**:
   $$
   (fg)(5) = f(5) \cdot g(5) = (-2(5)^{1/3}) \cdot (5(5)^{1/2})
   $$
   Evaluating this gives:
   $$
   (fg)(5) \approx -38.24
   $$

4. **Calculate $$ \left(\frac{f}{g}\right)(5) $$**:
   $$
   \left(\frac{f}{g}\right)(5) = \frac{f(5)}{g(5)} = \frac{-2(5)^{1/3}}{5(5)^{1/2}}
   $$
   Evaluating this gives:
   $$
   \left(\frac{f}{g}\right)(5) \approx -0.31
   $$

Now, rounding to two decimal places, we have:

- $$ (f + g)(5) \approx 7.76 $$
- $$ (f - g)(5) \approx -14.60 $$
- $$ (fg)(5) \approx -38.24 $$
- $$ \left(\frac{f}{g}\right)(5) \approx -0.31 $$

Thus, the final answers are:
- $$ (f + g)(5) = 7.76 $$
- $$ (f - g)(5) = -14.60 $$
- $$ (fg)(5) = -38.24 $$
- $$ \left(\frac{f}{g}\right)(5) = -0.31 $$
$$ (f + g)(5) = 7.76 $$, $$ (f - g)(5) = -14.60 $$, $$ (fg)(5) = -38.24 $$, $$ \left(\frac{f}{g}\right)(5) = -0.31 $$

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Algebra Questions